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PLOBIKTSOKT'S
PROGRESSIVE
PRIMARY ARITHMETIC,
FOB PRIMARY CLASSES
PUBLIC AND PRIVATE SCHOOLS.
EDITED BY
DANIEL W. FISH, A.M.
NEW YOEK :
IVISON, BLAKEMAN, TAYLOE & CO.
1870.
ROB IN SO IT'S
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and again in the year 1S63, by
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District of New York.
PKEFACE.
THIS primary work is designed for small children,
and as an easy introduction to the " Progressive Intel-
lectual Arithmetic," for advanced classes.
Its object is to lead the young pupil, by brief and
simple processes, applied to practical examples of easy
gradation, to acquire habits of thought and of reasoning,
in their simplest forms, and to draw out and strengthen
the mind by a progressive and almost imperceptible gra-
dation of thought and expression.
The operations of Adding and Subtracting, of Multi-
plying and Dividing, are first shown by pictorial objects ;
portions of the elementary tables are introduced at the
commencement of each lesson, and applied to short ex-
amples concerning familiar objects ; promiscuous reviews
of the elementary tables, and the more simple and easy
Denominate tables have been introduced. Fractions
have been treated as far as was thought practicable
in a work of this kind.
It is confidently believed that the progressive and
systematic arrangement, the simplicity and adaptation
to the juvenile mind, the typography and general attrac-
tiveness of this little book, will insure for it abundant
success.
THE AUTHOR.
(3)
SUGGESTIONS TO TEACHERS.
1. A TEACHER should have a particular time allotted
to every exercise, and regular lessons should be assigned,
to be recited each day at a specified hour.
2. Sufficient time being given the pupils to learn
their lessons, they should not be allowed the use of the
book at the time of recitation.
3. The teacher should first ascertain that the table is
thoroughly learned by every pupil in the class.
4. Each question should be slowly and distinctly read,
and the pupils be called upon promiscuously ; the pupil
called upon should stand erect, repeat the question, and
then give the solution. This will require close attention.
5. A correct and uniform analysis of each question
should be required from every pupil.
6. The class should be encouraged to detect and cor-
rect errors in the statement and solution of questions, to
be signified by raising the hand.
7. The teacher can extend the questions in each les-
son at pleasure, either by repeating those given, or
making additional ones.
(4)
-*
/ •'•••' ' •
PRIMARY ARITHMETIC.
LESSON I.
1. What is the first thing to be taught and learned in Arith-
metic ? ANS. Counting.
2. What is counting ? ANS. Expressing numbers by words.
3. What is a number r ANS. A unit, or a collection of units.
4. What is a unit ? ANS. A single thing.
5. How may numbers be expressed ? ANS. By words, letters,
and figures.
6. Which is the most common method ? ANS. By figures.
7. How many figures are used to express numbers ? ANS. Ten.
8. Name them.
ANS. Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
O H
9. Count the bells on each of the abo ,-e rows.
NOTATION AND NUMERATION.
LESSON II.
1. What is Notation? Ans. Writing num-
bers.
2. What is Numeration ? Ans. Reading
numbers.
3. How many letters are used to express
numbers ? Ans. Seven.
4. What are they ? Ans. I, V, X, L, C,
D, and M.
5. What is this method called ? Ans. The
Roman method.
6. Why is it so called? Ans. Because it
was first used by the Romans.
7. How many figures or characters are
used to express numbers ? Ans. Ten.
8. What are they ? Ans. 0, 1, 2, 3, 4, 5,
6, 7, 8, 9.
9. What is this method called? Ans.
The Arabic method.
10. Why is it so called ? Ans. Because
it was first used by the Arabs.
11. What may the ten figures used in ex-
pressing numbers be called? Ans. The
Arithmetical Alphabet.
12. Can all numbers be expressed by these
ten figures ? Ans. They can, by repeating
and combining them.
NOTATION AND NUMERATION.
1
LE
SSON III.
REMARK. — This lesson presents the printed and
written figures, and the Roman letters, by which num-
bers are commonly expressed. It should be carefully
studied by children, until they can read the figures with
facility when written on the black-board, or when they
meet with them in books.
Numbers.
Printed Written
Figures. Figures.
Roman
Letters.
Naught
0 0
One
i /
I
Two
2 2
II
Three
3 3
ni
Four
4 4
IV
Five
5 5
V
Six
6 6
VI
Seven
7 7
VII
Eight
8 g
VIII
Nine
9 - 9
IX
Ten
10 /tf
X
Eleven
11 //
XI
Twelve
12 /j>
XII
Thirteen
13 S3
XIII
Fourteen
14 44
XIV
Fifteen
15 ts
XV
Sixteen
16 st
XVI
Seventeen
17 //
XVII
Eighteen
18 4$
XVIII
Nineteen
19 4?
XIX
Twenty
20 so
XX
Twenty-one
21 9/
XXI
8 NOTATION AND NUMERATION.
L
ESSO
N IV.
Printed
Written
Roman
Numbers.
Figures.
Figures.
Letters.
Twenty-two
22
29
XXII
Twenty-three
23
S3
XXIII
Twenty-four
24
26
XXIV
Twenty-five
25
25
XXV
Twenty-six
26
26
XXVI
Twenty-seven
27
27
XXVII
Twenty-eight
28
2$
XXVIII
Twenty-nine
29
29
XXIX
Thirty
30
30
XXX
Thirty-one
31
3S
XXXI
Forty
40
40
XL
Forty-one
41
4S
XLI
Fifty
50
50
L
Fifty-one
51
5S
LI
Sixty
60
60
LX
Sixty-one
61
6<f
LXI
Seventy
70
70
LXX
Seventy-one
71
7S
LXXI
Eighty
80
$0
LXXX
Eighty-one
81
$s -
LXXXI
Ninety
90
90
XC
Ninety-one
91
9*
XCI
Ninety -two
92
92
XCII
One hundred
100
too
c
Two hundred
200
200
CO
Five hundred
500
500
D
One thousand
1000
4000
M
NOTATION AND NUMERATION.
LESSON V.
EEMARK. — The children should now be furnished
with slates and pencils, and required to read the follow-
ing numbers from the book, or when written on the
black-board by the teacher, and then to copy them on
their slates in straight columns.
1 11 21 31 41
2 12 22 32 42
3 13 23 33 43
4 14 24 34 44
5 -15 25 35 45
6 16 26 36 46
7 17 27 37 47
8 18 28 38 48
9 19 29 39 49
10 20 30 40 50
LESSON VI.
51* 61 71 81 91
52 62 72 82 92
53 63 73 83 93
54 64 74 84 94
55 65 75 85 95
56 66 76 86 96
57 67 77 87 97
58 68 78 88 98
' 59 69 79 89 99
60 70 80 90 100
10
ADDITION.
LESSON I.
Putting two or more numbers or things together into
one sum, is called ADDITION : thus,
and ¥J| more make
mug mug mugs.
9
i~ i
M and
i l
more make C
tree
trees
2 2
3. ^S<5^ and <§^^2^ more make
caps caps
3
trees.
4
pearsT
3 4
5. ^^y and NJ^\ more make
pens pens
pens.
6.
and
more
[II make
soldiers soldiers
soldiers.
ADDITION. 11
LESSON II.
1 and 1 are 2
1 and 2 are 3
1 and 3 are 4
1 and 4 are 5
1 and 5 are 6
1 and 6 are 7
1 and 7 are 8
1 and 8 are 9
1 and 9 are 10
1 and 10 are 11
1. If a slate pencil cost 1 cent, and an or-
ange 3 cents, how many cents will both cost ?
ANALYSIS. — TJiey will both cost as many cents as the
sum of 1 cent and 3 cents, which is 4 cents. Therefore
if a slate pencil cost 1 cent, and an orange 3 cents, they
will both cost 4 cents.
2. Sarah had 4 books, and her mother
gave her .1 more; how many books did she
then have?
3. In a garden are 1 plum tree and 6 pear
trees ; how many trees in the garden ?
4. A man gave 8 dollars for a coat, and 1
dollar for a hat ; how much did he give for
both?
5. In a class are 5 girls and 1 boy ; how
many pupils in the class ?
6. A boy gave 1 cent for a sponge, and 10
cents for a spelling book ; what did he give
for both?
7. Bought a broom for 1 shilling, and some
sugar for 9 shillings ; what did both cost ?
12 ADDITION.
LESSON III.
2 and 1 are 3
2 and 2 are 4
2 and 3 are 5
2 and 4 are 6
2 and 5 are 7
2 and 6 are 8
2 and 7 are 9
2 and 8 are 10
2 and 9 are 11
2 and 10 are 12
1. James rode 2 miles in the stage, and 4
miles in the cars; how far did he ride in
both?
ANALYSIS. — He rode as many miles as the sum of
2 miles and 4 miles, which is 6 miles. Therefore, since
James rode 2 miles in the stage and 4 miles in the cars,
he rode 6 miles in both.
2. If a barrel of cider cost 2 dollars, and a
barrel of flour 7 dollars, what will both cost ?
3. A man had 2 sons and 5 daughters to
support; how many children had he?
4. A lady gave 2 cents for some ribbon,
and 10 cents for a comb; what did she pay
for both ?
5. A farmer sold a sheep for 2 dollars, and
a hog for 9 dollars ; what did he get for both ?
.6. John went to the river to fish, and
caught 2 trout and 8 perch ; how many fish
did he catch ?
7. If a boy spend 2 cents and have 2 left,
how many cents had he at first ?
ADDITION. 13
LESSON IV.
3 and 1 are 4
3 and 2 are 5
3 and 3 are 6
3 and 4 are 7
3 and 5 are 8
3 and 6 are 9
3 and 7 are 10
3 and 8 are 11
3 and 9 are 12
3 and 10 are 13
1. Frank picked 3 ripe plums from one
tree, and 5 from another ; how many did he
pick from both ]
ANALYSIS. — As many plums as the sum of 3 plums
and 5 plums, which is 8 plants. Therefore, since Frank
picked 3 plums from one tree, and 5 from another, he
picked 8 plums both.
2. A grocer sold 3 pounds of sugar to one
man, and 4 to another; how many pounds
did he sell to both ?
3. Mary bought an inkstand for 7 cents,
and some paper for 3 cents ; how much did
she pay for both ?
4. A beggar received 6 cents from one lit-
tle girl, and 3 from another ; how many cents
did he receive from both ?
5. A boy found two hen's nests ; in one
were 8 eggs, in the other 3 eggs ; how many
srs were there in both nests ?
6. A knife cost 9 cents, and a top 3 cents ;
what did they both cost I
14 ADDITION.
LESS
ON V. %
4 and 1 are 5
4 and 6 are 10
4 and 2 are 6
4 and 7 are 11
4 and 3 are 7
4 and 8 are 12
4 and 4 are 8
4 and 9 are 13
4 and 5 are 9
4 and 10 are 14
1. Henry had 4 cents in one hand and 3
cents in the other; how many cents had he
in both ?
ANALYSIS. — As many cents in both as the sum of 4
cents and 3 cents, which is 7 cents. Therefore, since
Henry had 4 cents in one hand, and 3 cents in the other.
he had 1 cents in both.
2. If a skein of silk cost 4 cents, and a
yard of tape 6 cents, how much do both cost?
3. A farmer has 4
black sheep, and 8
white ones ; how many sheep has he of both
kinds 1
4. There are 5 birds on one tree, and 4 on
another ; how many birds are there on both
trees I
5. Rollin had 4 books, and his father gave
him 4 more ; how many books had he then ?
6. If a lady paid 7 dollars for a dress, and
4 for a bonnet, what did she pay for both ]
7. There are 4 books on one shelf, and 9 on
another ; how many books on both shelves ?
ADDITION.
15
LESSON VI.
5 and 1 are 6
5 and 2 are 7
5 and 3 are 8
5 and 4 are 9
5 and 6 are 11
5 and 7 are 12
5 and 8 are 13
5 and 9 are 14
5 and 5 are 10 5 and 10 are 15
1. A miller sold 5 barrels of flour at one
time, and 4 barrels at another; how many
barrels did he sell in all]
2. George lost 2 cents, and had 5 cents
left; how many cents had he at first]
3. Gave 5 cents for a writing book, and
3 cents for a pen holder; what was the cost
of both?
4. A boy had 7 peaches in his basket, and
his sister put in 5 more ; how many peaches
had he then I
5. Joseph rode 6 miles, and walked 5
miles ; how far did he go ?
6. Carrie had 5 roses, and Nellie had 8 ;
how many roses had both ?
7. A merchant sold 5 yards of calico at
one time, and 5 at another ; how many yards
did he .sell in all ?
8. A farmer paid 10 dollars for a plow> and
5 dollars for a harrow ; how much did he pay
for both ]
» -
16 ADDITION.
LESSON VII.
6 and 1 are 7
6 and 2 are 8
6 and 3 are 9
6 and 4 are 10
6 and 5 are 11
6 and 6 are 12
6 and 7 are 13
6 and 8 are 14
6 and 9 are 15
6 and 10 are 16
1. A boy, after losing 6 marbles, had 4
left ; how many had he at first \
2. Albert spent 6 cents, and had 5 left;
how many had he at first I
3. A man paid 3 dollars for a barrel of
cider, and 6 dollars for a barrel of flour;
what did he pay for both 1
4. A gardener picked 6 peaches from one
tree, and 7 from another ; how many peaches
did he pick from both I
5. Dick caught 2 gray squirrels, and 6
red ones ; how many did he catch in all 1
6. A cabinet maker asks 6 dollars for a
rocking chair, and 6 dollars for a table ; what
is the cost of both 1
7. In the fruit dish are 6 red apples and
9 green ones ; how many apples in the
dish \
8. Edwin is 6 years old, and his sister
Martha is 10 years older; what is the age
of Martha \
ADDITION. 17
LESSON VIII.
7 and 1 are 8
7 and 2 are 9
7 and 3 are 10
7 and 4 are 11
7 and 5 are 12
7 and 6 are 13
7 and 7 are 14
7 and 8 are 15
7 and 9 are 16
7 and 10 are 17
1. Bought a ton of hay for 7 dollars, and
some oats for 6 dollars ; what was the cost
of both]
2. David gathered 3 quarts of walnuts,
and Homer 7 quarts ; how many quarts did
both gather ?
3. Howard had 7 rabbits, and Herbert
gave him 2 more ; how many had he then I
4. A farmer picked 5 bushels of apples
from one tree, and 7 bushels from another ;
how many bushels did he gather from both ?
5; Asa is 8 years old ; how old will he be
7 years from this time ]
6. In a basket are 7 bunches of green
grapes and 7 bunches of purple ones; how
many bunches of both I
7. If a boy earn 7 shillings in one week,
and 9 shillings the next, how many shillings
will he earn in 2 weeks'?
8. In a shop, 2 men and 7 boys are em-
' ployed ; how many persons are employed ?
18 ADDITION.
LESSON IX.
8 and 1 are 9
8 and 2 are 10
8 and 3 are 11
8 and 4 are 12
8 and 5 are 13
8 and 6 are 14
8 and 7 are 15
8 and 8 are 16
8 and 9 are 17
8 and 10 are 18
1. Henry hoed 8 rows of corn one day,
and 5 the next ; how many rows did he hoe
in both days I
2. Andrew had 8 apples and 8 peaches in
his basket ; how many had he of both ?
3. There are 3 gentlemen and 8 ladies in
a boat ; how many persons in the boat ]
4. A man had 8 dollars, and borrowed 6
more ; how many dollars had he then 1
5. Bought a pound of raisins for 9 cents,
and a pound of sugar for 8 cents ; what was
the cost of both ]
6. Emily had 7 white roses and 8 red
ones; how many roses had she of both
kinds ?
7. A boy sold 8 boxes of matches to one
man, andw 4 boxes to another ; how many
boxes did he sell to both ]
8. There are 10 shade trees now in the
park, and 8 have been cut down; how
many trees were set out I
ADDITION. 19
LESSON X,
9 and 1 are 10
9 and 2 are 11
9 and 3 are 12
9 and 4 are 13
9 and 6 are 15
9 and 7 are 16
9 and 8 are 17
9 and 9 are 18
9 and 5 are 14 9 and 10 are 19
1. If a firkin of butter is worth 9 dollars,
and a cord of wood 6 dollars, what are both
worth ?
2. A lady bought a muff for 9 dollars,
and a hat for 5 dollars ; what did she pay
for both ?
3. Cora read 10 pages of history, and 9
pages of poetry ; how many pages did she
read in all ]
4. A traveler paid 9 shillings a day for
his board, and 7 shillings a day for his horse ;
how much did he pay for both ?
5. Annie, had 9 pictures, and her brother
gave her 2 more ; how many had she then 1
6. If a peck of apples cost 9 cents, and a
head of cabbage 4 cents, what will both cost ?
7. In a certain class there are 9 boys and
8 girls ; how many scholars are there in the
class 1
8. There are 9 geese and 9 ducks swim-
ming in a pond ; how many of both 1
20 ADDITION.
LESSON XI.
10 and 1 are 11
10 and 2 are 12
10 and 3 are 13
10 and 4 are 14
10 and 5 are 15
10 and 6 are 16
10 and 7 are 17
10 and 8 are 18
10 and 9 are 19
10 and 10 are 20
1. If a man give 10 dollars for a harness,
and 4 dollars for a whip, how much does he
give for both ?
2. A farmer has 10 sheep in one lot, and
9 in another ; how many has he in both ?
3. A tailor sold a coat for 10 dollars, and
a pair of pantaloons for 6 dollars; how much
did he receive for both 1
4. A beggar met two boys ; one gave him
10 cents, and the other 7 cents ; how many
cents did they both give him ?
5. There were 8 boys on one bench, and
10 on another; how many boys on both
benches 1
6. Alice had 10 cents, and her mother
gave her 2 more ; how many had she then ?
7. Bought a pig for 3 dollars, and a calf
for 10 dollars ; how much did I pay for both ]
8. Charles picked 10 pears from a tree,
and left 10 on it; how many were on the
tree at first 1
ADDITION. 21
LESSON XII.
PROMISCUOUS REVIEW.
2 and 5 are how many?
7 and 9 are how many?
6 and 2 are how many?
6 and 5 are how many ?
2 and 4 are how many?
3 and 6 are how many?
8 and 9 are how many ?
4 and 4 are how many ?
9 and 4 are how many?
7 and 8 are how many ?
4 and 7 are how many?
9 and 3 are how many?
8 and 6 are how many?
2 and 9 are how many?
6 and 3 are how many?
5 and 4 are how many?
7 and 2 are bow many?
3 and 8 are how many ?
3 and 3 are how many?
5 and 6 are how many?
3 and 9 are how many?
5 and 8 are how many?
4 and 5 are how many ?
4 and 2 are how many ?
9 and 8 are how many?
3 and 7 are how many?
8 and o are how many?
6 and 4 are how many?
4 and 9 are how many ?
7 and 6 are how many?
5 and 4 are how many ?
6 and 8 are how many?
2 and 7 are how many ?
9 and 5 are how many ?
7 and 5 are how many?
8 and 3 are how many?
2 and 3 are how many?
9 and 6 are how many?
5 and 2 are how many?
5 and 7 are how many?
6 and 9 are how many?
4 and 6 are how many?
7 and 7 are how many?
7 and 3 are how many?
3 and 4 are how many?
2 and 8 are how many ?
8 and 7 are how many?
5 and 9 are how many?
4 and 8 are how many ?
8 and 8 are how many ?
9 and 2 are how many?
6 and 7 are how many?
5 and 3 are how many?
5 and 5 are how many?
6 and 6 are how many?
9 and 7 are how many?
3 and 5 are how many?
2 and 6 are how many ?
7 and 4 are how many?
9 and 9 are how many?
22 ADDITION.
LESSON XIII.
PEOMISCUOUS EXAMPLES.
1. Henry paid 6 cents for an inkstand, 4
cents for some pens, and 5 cents for a writing
book ; how much did he pay for all I
ANALYSIS. — He paid as many cents as the sum of 6
cents, 4 cents, and 5 cents ; 6 cents and 4 cents are 10
cents, and 6 cents are 15 cents. Therefore, fyc.
2. A drover bought 4 cows of one man, 3
of another, and 7 of another ; how many cows
did he buy in all I
3. Elizabeth gave 10 cents for three spools
of thread, b cents for a thimble, and 9 cents
for some needles ; how many cents did she
give for all I
4. A lady bought a dress for 8 dollars, a
shawl for 9 dollars, and a parasol for 2 dollars ;
how many dollars did she pay for them all ?
5. If a man paid 6 dollars for a cord of
wood, 5 dollars for a ton of hay, 7 dollars
for some pork, and 3 dollars for some beef,
how many dollars did he pay for the whole ?
6. A boy traveled 6 miles one day, 8 miles
the next day, and 10 miles the next ; how
many miles did he travel in three days 1
7. A cabinet maker asked 12 dollars for a
bureau, 10 dollars for a table, and 5 dollars
for a stand ; what was his price for the whole 1
SUBTRACTION.
23
LESSON I.
Finding the difference between two numbers of the
same kind, is called SUBTRACTION.
1. £T^ taken from ^
m^f^fiif^ . K •
rabbit
leaves l
rabbits, rabbit
1 3 2
2. H taken from (g) Qg ieaves
hat hats, hats.
2 42
3- D o takenfrom OO(OD) leaves 00
eggs eggs, eggs.
tulips
3
glasses
birds
taken from
taken from
taken from •
\ leaves I
tulips,
5
glasses,
4
birds,
tulips.
leaves how
many?
leaves how
many?
24 SUBTRACTION.
LESSON II.
1 from 1 leaves 0
1 from 2 leaves 1
1 from 3 leaves 2
1 from 4 leaves 3
1 from 5 leaves 4
1 from 6 leaves 5
1 from 7 leaves 6
1 from 8 leaves 7
1 from 9 leaves 8
1 from 10 leaves 9
1. A boy, having 3 apples, gave 1 to his
sister ; how many had he left ?
ANALYSTS. — He had as many apples left as the dif-
ference between 3 apples and 1 apple, which is 2 apples.
Therefore, since a boy had 3 apples, and gave 1 apple to
his sister, he had 2 apples left.
2. A poor woman who had 6 cents, lost 1 ;
how many had she left I
3. A tailor had 7 yards of cloth ; he cut
off 1 yard ; how many yards had he left ?
4. Mary had 8 credit marks, and 1 de-
merit mark ; how many more credit than
demerit marks had she?
5. Robert found 5 ripe pears under a tree,
and ate 1 of them ; how many had he left 1
6. If you make 10 marks on your slate,
and rub out 1, how many remain ?
7. If I pay 4 dollars for a barrel of
flour, and 1 dollar for a bushel of corn, how
much more do I pay for the flour than for
the corn ?
SUBTRACTION. 25
LESSON III.
2 from 2 leaves 0
9 from 3 leaves 1
2 from 4 leaves 2
2 from 5 leaves 3
2 from 6 leaves 4
2 from 7 leaves 5
2 from 8 leaves 6
2 from 9 leaves 7
2 from 10 leaves 8
2 from 11 leaves 9
1. Alice had 4 peaches, and gave 2 to
Rollin ; how many had she left 1
ANALYSIS. — She had as many peaches left as the dif-
ference between 4 peaches and 2 peaches, which is 2
peaches. Therefore, since Alice had 4 peaches, and gave
2 to Rollin, she had 2 peaches left.
2. Lucy had 6 sheets of paper, and gave 2
to Ann ; how many had she left I
3. There were 8 pigeons on a tree, and 2
flew away ; how many were there left ?
4. Frank had 2 apples when he started
for school ; he gave 2 away ; how many had
he left 1
5. Ella had 5 roses, and gave 2 to her
teacher; how many had she left?
6. Clinton had 7 chickens, and a cat
caught 2 of them ; how many had he left ?
7. A tinner had 3 milk pails, and sold 2
of them ; how many had he left ?
8. Willie had 9 cents, and gave 2 cents
to a blind man ; how many had he left ?
26 SUBTRACTION.
LESSON IV.
3 from 3 leaves 0
3 from 4 leaves 1
3 from 5 leaves 2
3 from 6 leaves 3
3 from 7 leaves 4
3 from 8 leaves 5
3 from 9 leaves 6
3 from 10 leaves 7
3 from 11 leaves 8
3 from 12 leaves 9
1. Mr. Jones sold some hay for 7 dollars,
and received 3 dollars ; how much more was
due ?
ANALYSIS. — As much more was due as the difference
between 7 dollars and 3 dollars, which is 4 dollars.
Therefore, since Mr. Jones sold some hoy for 7 dollars,
and received 3 dollars, there were four dollars more due.
2. Samuel found 5 eggs, and broke 3 of
them ; how many had he left 1
3. Marcus borrowed 10 cents, and paid 3 ;
how much did he then owe 1
4. A merchant bought 9 barrels of flour,
and sold all but 3 barrels ; how many did he
selH
5. A man had 12 sheep in a pasture, and
3 of them jumped out ; how many remained?
6. Daniel had 3 apples, and gave each of
his three sisters one apiece ; how many had
he left ?
7. A farmer had 6 horses, and sold all but
3 ; how many did he sell ]
SUBTRACTION. 27
LESSON V.
4 from 4 leaves 0
4 from 5 leaves 1
4 from 6 leaves 2
4 from 7 leaves 3
4 from 8 leaves 4
4 from 9 leaves 5
4 from 10 leaves 6
4 from 11 leaves 7
4 from 12 leaves 8
4 from 13 leaves 9
1. A farmer, having 8 pigs, sold 4 of
them ; how many had he left 1
ANALYSIS. — He had as many pigs left as the differ-
ence between 8 pigs and 4 pigs, which is 4 pigs. There-
fore, since a farmer had 8 pigs, and sold 4 of them, he
had 4 pigs left.
2. A boy caught 10 fishes, and threw 4
of them back into the creek ; how many had
he left ?
3. Bought a saddle for 13 dollars, and a
bridle for 4 dollars ; how much more did I
pay for the saddle than for the bridle 1
4. There were 9 passengers in the stage, 4
of whom got out ; how many remained in
the stage I
5. Laura found 11 roses on her bush ; and
picked 4 ; how many remained on the bush ?
6. A man paid 6 shillings for his dinner,
and 4 shillings for his breakfast; how much
more did he pay for his dinner than for his
breakfast I
28 SUBTRACTION.
LESSON VI.
5 from 5 leaves 0
5 from 6 leaves 1
5 from 7 leaves 2
5 from 8 leaves 3
5 from 9 leaves 4
5 from 10 leaves 5
5 from 11 leaves 6
5 from 12 leaves 7
5 from 13 leaves 8
5 from 14 leaves 9
1. A man earned 7 dollars in a week, and
spent 5 dollars of it ; how many did he save?
2. If 10 gallons of water run into a cistern
in a minute, and 5 gallons run out, how
many remain]
3. A peddler had 8 penknives, and sold 5
of them ; how many had he left]
4. Alfred fired into a flock of 12 wild
pigeons, and killed 5 of them; how many
flew away]
5. A woman bought 14 yards of calico,
and used 5 yards ; how many yards had she
left ]
6. Carlos, having 11 cents, gave 5 of them
for an orange ; how many had he left ]
7. Stephen caught 13 fish, and gave 5 of
them to a poor woman ; how many had he
left]
8. On a rose bush are 6 white roses, and
Eliza picks 5 of them for the flower vase ;
how many are left on the bush ]
SUBTRACTION. 29
LESSON VII,
6 from 6 leaves 0
6 from 7 leaves 1
6 from 8 leaves 2
6 from 9 leaves 3
6 from 10 leaves 4
6 from 11 leaves 5
6 from 12 leaves 6
6 from 13 leaves 7
6 from 14 leaves 8
6 from 15 leaves 9
1. A boy gave 14 cents for a knife, and
sold it for 6 cents ; how much did he lose ]
2. In a spelling class are 7 girls and 6
boys ; how many more girls than boys in the
class 1
3. A merchant bought 9 barrels of salt,
and after selling some, he found he had
6 barrels left ; how many barrels did he
sell?
4. If I owe 15 dollars, and pay 6 dollars,
how much do I still owe ?
5. Stephen had 13 marbles, and lost 6 of
them ; how many had he left ?
6. There are 12 sheep in a yard, and a
dog bites all but 6 of them; how many does
he bite ?
7. Arthur rode 1 1 miles in the cars, and 6
in the stage ; how many more miles did he
ride in the cars than in the stage ?
8. Carrie has 6 roses, and ^ives 6 to her
teacher ; how many has she left ?
30 SUBTRACTION.
LESSON VIII.
7 from 7 leaves 0
7 from 8 leaves 1
7 from 9 leaves 2
7 from 10 leaves 3
7 from 12 leaves 5
7 from 13 leaves 6
7 from 14 leaves 7
7 from 15 leaves 8
7 from 11 leaves 4 7 from 16 leaves 9
1. Edgar had 12 chickens, and a cat
killed 7 of them ; how many chickens had
he left]
2. Julius had 7 cents, and his father gave
him enough more to make 15 ; how many
cents did his father give him ?
3. A young lady went shopping with
16 dollars ; when she returned she had
only 7 dollars; how much money did she
spend ]
4. During 13 days, it rained 7 days; how
many fair days were there ]
5. In a class of 11 scholars, 7 recited per-
fect lessons; how many had imperfect les-
sons ]
6. In a yard there were 9 shade trees, and
the wind blew down 7 ; how many were
left standing 1
7. A man bought a calf for 7 dollars, and
sold it for 10 dollars ; how much did he
gain ?
SUBTRACTION. 81
LESSON IX.
8 from 8 leaves 0
8 from 9 leaves 1
8 from 10 leaves 2
8 from 11 leaves 3
8 from 12 leaves 4
8 from 13 leaves 5
8 from 14 leaves 6
8 from 15 leaves 7
8 from 16 leaves 8
8 from 17 leaves 9
1. A farmer, having 15 sheep, sold 8 of
them ; how many had he left ?
2. Thornton had 9 merit marks, and 8
dement marks ; how many more merit than
demerit marks had he ?
3. Peter carried 10 quarts of berries to
market, and sold 8 quarts ; how many quarts
had he left]
4. A man sold a cow for 17 dollars, and
took a plow worth 8 dollars, and the bal-
ance in money; how much money did he
receive ?
5. There were 14 yards in a piece of me-
rino, and a lady bought 8 yards for a dress ;
how many yards were left I
6. In a row of 12 shade trees, 8 of them
die ; how many are left ?
7. Calvin, having 16 cents, paid 8 cents
for a slate ; how many had he left ?
8. Emma is 11 years old, and Willie 8;
what is the difference in their ages ?
32 SUBTRACTION.
LESSON X.
9 from 9 leaves 0
9 from 10 leaves 1
9 from 11 leaves 2
9 from 12 leaves 3
9 from 13 leaves 4
9 from 14 leaves 5
9 from 15 leaves 6
9 from 16 leaves 7
9 from 17 leaves 8
9 from 18 leaves 9
1. James sold his colt for 16 dollars, and
received in payment 9 dollars' worth of goods,
and the rest in money ; how much money did
he receive?
2. Clorinda had 10 cents, and gave 9
cents for a new slate ; how many cents had
she left I
3. A painter bought 11 gallons of oil, and
after using 9 gallons, sold the remainder;
how much did he sell ?
4. A grocer bought a quantity of butter
for 12 dollars, and it being damaged, he was
obliged to sell it for 9 dollars ; how much
did he lose by the bargain ?
5. Austin, having 15 steel pens, gave away
all but 9 of them; how many did he give
away ?
6. A man borrowed 14 dollars, and paid 9
of it ; how much did he still owe I
7. A farmer had 9 sheep, and bought
enough to make 18 ; how many did he buy]
SUBTRACTION. 33
LESSON XI.
10 from 10 leaves 0
10 from 11 leaves 1
10 from 12 leaves 2
10 from 13 leaves 3
10 from 14 leaves 4
10 from 15 leaves 5
10 from 16 leaves 6
10 from 17 leaves 7
10 from 18 leaves 8
10 from 19 leaves 9
1. Ealph earned 17 cents and received 10
cents; how much is still due himl
2. In a certain school are 18 girls and 10
boys ; how many more girls than boys are
there ?
3. A grocer had 12 boxes of lemons, and
sold 10 boxes; how many boxes had he
left?
4. In a school there are 10 boys and 16
girls ; how many more girls than boys ?
5. Ella had 14 roses, and gave away 10 of
them ; how many had she left ?
6. A man bought a keg of molasses con-
taining 15 gallons; having used a part of it,
he found there were 10 gallons left; how
many gallons did he use I
7. Edgar had 19 cents, and spent 10 of
them ; how many cents had he left ?
8. A fanner had 13 acres of wheat, and
10 acres of corn ; how many acres more of
wheat had he than of corn ?
SUBTRACTION.
LESSON XII.
PROMISCUOUS REVIEW.
5 from
2 from
5 from
9 from
6 from
7 from
9 from
4 from
5 from
6 from
8 from
7 from
6 from
2 from
3 from
5 from
9 from
9 from
7 from
2 from
3 from
7 from
8 from
4 from
2 from
7 from
3 from
5 from
9 from
8 from
14 how
8 how
9 how
many?
many?
many ?
10 how many?
many ?
many ?
many ?
many ?
many ?
many ?
how
12 how
12 how
8 how
10. how
11 how
9 how
16 how
9 how
how
how
8 how
14 how
13 how
9 how
10 how
11
7
many :
many ?
many?
many ?
many ?
many ?
many ?
many ?
many ?
many?
9 how
15 how
17 how
10 how
9 how
14 how
11 how
13 how
17 how
14 how
many :
many?
many?
many?
many?
many ?
many?
many ?
many?
many ?
6 from
4 from
8 from
5 from
7 from
3 from
3 from
9 from
6 from
8 from
4 from
3 from
5 from
7 from
8 from
9 from
7 from
6 from
5 from
4 from
8 from
9 from
7 from
4 from
3 from
6 from
9 from
8 from
6 from
4 from
14 how
7 how
15 how
11 how
10 how
8 how
13 how
1 1 how
12 how
10 how
11 how
10 how
12 how
13 how
12 how
16 how
8 how
13 how
7 how
many r
many?
many?
many?
many ?
many?
many ?
many ?
many ?
many?
many r
many ?
many?
many ?
many?
many ?
many?
many?
many F
12 how many?
16 how
15 how
11 how
9 how
12 how
15 how
18 how
1 1 how
10 how
13 how
many r
many ?
many ?
many ?
many?
many ?
many?
many?
many ?
many?
SUBTRACTION. 35
LESSON XIII.
PROMISCUOUS EXAMPLES.
1. Oscar had 16 cents; he gave 6 cents
to a beggar, and 5 cents for an orange ; how
many had he left ?
ANALYSIS. — He had left the difference between 16
cents, and the sum of 6 cents and 5 cents ; 6 cents and 5
cents are 11 cents, and 11 cents from 16 cents leaves 5
cents. Therefore, fyc.
2. A farmer, having 18 sheep, sold 7 at
one time, and 4 at another ; how many had
he left ?
3. A grocer bought 10 dozen of eggs of
one man and 9 dozen of another; he then
sold 6 dozen to one of his neighbors, and
kept the rest for his own use ; how many
did he keep ?
4. A farmer bought a cow for 15 dollars ;
he paid one 10 dollar bill, and one 3 dollar
bill ; how much did he still owe ?
5. A boy, having 17 chickens, sold 5 of
them at one time, 7 at another, and 2 at an-
other ; how many had he left ?
6. Sold some pork for 12 dollars, and
received some sugar worth 3 dollars, a hat
worth 2 dollars, some cloth worth 4 dollars,
arid the rest in money; how much money
did I receive ?
36
MULTIPLICATION.
LESSON I.
MULTIPLICATION is taking one number as many times
as there are units in another : thus,
1. If 2 boys have 2 apples apiece, how many apples
will both have ?
Two times two are how many ?
2. If there are 3 combs in one box, how many combs
would there be in 2 boxes ?
lil if If W I
Two times three are how many ?
3. If 3 men have 2 dogs each, how many dogs will
they all have ?
Three times two are how many ?
4. If 1 man can make 2 boots in three days, how
many boots can 4 men make ?
Two times four are how many ?
5. If there are 3 owls in each of 3 cages, how many
owls in all ?
Three times three are how many ?
MULTIPLICATION. 37
LESSON II
once 1 is 1
once 2 is 2
once 3 is 3
once 4 is 4
once 5 is 5
once 6 is 6
once 7 is 7
once 8 is 8
once 9 is 9
once 10 is 10
1. At 1 cent each, what will 2 eggs cost?
ANALYSIS. — Since 1 egg cost 1 cent, 2 eggs, which
are 2 times 1 ego, will cost 2 times 1 cent, which are 2
cents. Therefore, at 1 cent each, 2 eggs will cost 2
cents.
2. If a man earn 1 dollar a day, how much
can he earn in 4 days ?
3. If Rollin reads 1 hour each evening,
how many hours will he read in 6 even-
ngs
4. What will 5 bushels of wheat cost, at
1 dollar a bushel ?
5. At 1 cent each, what will 9 steel pens
cost?
6. If a family eat 1 bushel of corn in a
week, how many bushels would they eat in
10 weeks ?
7. If Thomas gets 1 credit mark a day,
how many credit marks will he get in 7 days ?
8. If Henry write 1 page a day, how
many pages will he write in 8 days ?
38 MULTIPLICATION.
LESSON III,
2 times 1 are 2
2 times 2 are 4
2 times 3 are 6
2 times 4 are 8
2 times 5 are 10
2 times 6 are 12
2 times 7 are 14
2 times 8 are 16
2 times 9 are 18
2 times 10 are 20
1. What will 2 pounds of rice cost, at 6
cents a pound ]
ANALYSIS. — Since 1 pound costs 6 cents, 2 pounds,
which are 2 ft'mes 1 pound, will cost 2 ta'mes 6 ce/zte,
which are 12 mite. Therefore 2 pounds of rice will
cost 12 cerate, a£ 6 cents a pound.
2. Sarah gave 2 girls 3 apples apiece;
how many did she give them both I
3. If on one rose bush there are 4 roses,
how many on 2 busher ]
4. Almira bought 2 yards of ribbon at 5
cents a yard ; how much did she pay for the
whole ?
5. At 7 cents a pound, what will 2 pounds
of sugar cost ]
6. What will 2 tons of hay cost, at 9 dol-
lars a ton ?
7. At 5 shillings a bushel, what will be
the cost of 2 bushels of corn ?
8. At 2 cents apiece, what will 2 pears
cost?
MULTIPLICATION. 39
LESSON IV.
3 times 1 are 3
3 times 2 are 6
3 times 3 are 9
3 times 4 are 12
3 times 5 are 15
3 times 6 are 18
3 times 7 are 21
3 times 8 are 24
3 times 9 are 27
3 times 10 are 30
1. If a man earn 9 dollars in one week,
how many dollars will he earn in 3 weeks ?
ANALYSIS. — If a man earn 9 dollars in 1 week, in
3 weeks, which are 3 times 1 week, he will earn 3 times
9 dollars, which are 27 dollars. Therefore, if a mon
earn 9 dollars in 1 week, he will earn 27 dollars in 3
weeks.
2. If a farmer give 4 bushels of corn for
one yard of cloth, how many bushels must
he give for 3 yards 1
3. At 8 shillings a yard, what will 3 yards
of silk cost ?
4. In one cent are 10 mills; how many
mills in 3 cents 1
5. When sugar is worth 7 cents a pound,
what will 3 pounds cost I
6. A drover paid 3 dollars a head for
sheep ; how much did he pay for 3 sheep I
7. Egbert gave three of his classmates 5
apples apiece ; how many apples did he give
them all ?
40 MULTIPLICATION.
LESSON V.
4 times 1 are 4
4 times 2 are 8
4 times 3 are 12
4 times 4 are 16
4 times 5 are 20
4 times 6 are 24
4 times 7 are 28
4 times 8 are 32
4 times 9 are 36
4 times 10 are 40
1. What will 4 yards of ribbon cost, at 4
cents a yard ]
ANALYSIS. — Since 1 ^are? of ribbon costs 4 cerate,
4 yards, which are 4 ta'wes 1 yarof, will cost 4 ft'frais 4
cents, which are 1 6 cents. Therefore, 4 yards of ribbon,
at 4 ce/ite a yard, will cost 1 6 cents.
2. If a horse eat 8 quarts of oats a day,
how many quarts will he eat in 4 days ?
3. At 9 shillings a day, what will 4 days'
work come to 1
4. If one bench will seat 6 pupils, how
many pupils will 4 benches seat ?
5. Martha's dress contains 7 yards of mus-
lin, at 4 shillings a yard ; what was the cost
of the dress I
6. If Joseph walk 3 miles in an hour,
how far will he walk in 4 hours ?
7. A butcher bought 4 calves at 5 dollars
apiece ; what did they cost ?
8. At 2 shillings a quart, what will 4
quarts of molasses cost]
MULTIPLICATION. 41
LESSON VI.
5 times 1 are 5
5 times 2 are 10
5 times 3 are 15
5 times 4 are 20
5 times 5 are 25
5 times 6 are 30
5 times 7 are 35
5 times 8 are 40
5 times 9 are 45
5 times 10 are 50
1. There are 7 days in 1 week ; how many
days in 5 weeks ?
2. How far will a boat sail in 5 hours, at
at the rate of 9 miles an hour ?
3. What will 5 barrels of flour cost, at 5
dollars a barrel I
4. How many yards are there in 5 pieces
of cloth, if there are 10 yards in each piece 1
5. If an orange is worth 4 apples, how
many apples are 5 oranges worth?
6. If a pupil work 6 problems a day, how
many problems will he work in 5 days ?
7. Carlos gave 5 beggars 5 cents apiece ;
how many cents did he give them all I
8. If a horse travel 8 miles an hour, how
far can he travel in 5 hours I
9. Which is greater, 5 times 8, or 4 times
10?
10. Which is greater, 4 times 6, or 3
times 8 ? 5 times 6, or 3 times 10 ? 5 times
8, or 4 times (J 1
42 MULTIPLICATION.
LESSON VII.
6 times 1 are 6
6 times 2 are 12
6 times 3 are 18
6 times 4 are 24
6 times 5 are 30
6 times 6 are 36
6 times 7 are 42
6 times 8 are 48
6 times 9 are 54
6 times 10 are 60
1. A farmer bought a plow for 5 dollars ;
what would 6 plows cost at the same rate I
2. At 2 dollars a day, how many dollars
would a man earn in 6 days ]
3. What cost 6 tons of hay, at 7 dollars
a ton ?
4. George bought 6 lemons at 4 cents
apiece ; what did they all cost ?
5. There are 8 quarts in 1 peck ; how
many quarts in 6 pecks I
6. What will 6 pounds of honey cost, at
10 cents a pound I
7. What will 6 pounds of ginger cost at 6
cents a pound]
8. In a garden are 6 apple trees, and 4
bushels of apples on each tree; how many
bushels on all the trees ]
9. Which is greater, 6 times 1, or 0
times 6 1
10. Which is greater, 6 times 5, or 3
times 10 I
MULTIPLICATION. 43
LE SSON VIII.
7 times 1 are 7
7 times 2 are 14
7 times 3 are 21
7 times 4 are 28
7 times 5 are 35
7 times 6 are 42
7 times 7 are 49
7 times 8 are 56
7 times 9 are 63
7 times 10 are 70
1. If a mill grind 5 bushels of wheat an
hour, how many bushels will it grind in 7
hours I
2. When wheat is worth 2 dollars a bushel,
what will 7 bushels cost ?
3. In New England, 6 shillings make a
dollar ; how many shillings in 7 dollars I
4. If you write 8 lines in a day, how many
lines will you write in 7 days 1
5. At 10 dollars a month, how many dol-
lars will a man earn in 7 months ?
6. What will be the cost of 7 barrels of
flour, at 7 dollars a barrel 1
7. What are 7 quarts of cherries worth,
at 4 cents a quart 1
8. At 9 shillings a bushel, what will 7
bushels of peaches cost ?
9. If there are 3 sheets of paper in one
writing book, how many sheets in 7 books ?
10. Which is greater, 7 times 6, or 6
times 7 I
44 MULTIPLICATION.
LESSON IX.
8 times 1 are 8
8 times 2 are 16
8 times 3 are 24
8 times 4 are 32
8 times 5 are 40
8 times 6 are 48
8 times 7 are 56
8 times 8 are 64
8 times 9 are 72
8 times 10 are 80
1. If a ton of hay cost 7 dollars, what
will 8 tons cost ?
2. In New York, 8 shillings make a dol-
lar; how many shillings in 5 dollars'?
3. When coffee is worth 10 cents a pound,
what will be the cost of 8 pounds I
4. At 4 cents a pound, what will 8 pounds
of rice cost I
5. What will 8 hats cost, at 3 dollars
apiece ]
6. In one square yard are 9 square feet ;
how many square feet in 8 square yards 1
7. What will 8 bushels of potatoes cost,
at 6 dimes a bushel ?
8. At 6 dollars a barrel, what will 8 bar-
rels of flour cost ?
9. What is the difference between 8 times
7, and 7 times 8?
10. At 8 cents a pound, what will 8
pounds of soda cost ]
11. What cost 2 slates, at 8 cents apiece?
MULTIPLICATION. 45
LESSON X.
9 times 1 are 9
9 times 2 are 18
9 times 3 are 27
9 times 4 are 36
9 times 5 are 45
9 times 6 are 54
9 times 7 are 63
9 times 8 are 72
9 times 9 are 81
9 times 10 are 90
1. If a man travel by stage 5 miles an
hour, how far will he travel in 9 hours I
2. What cost 9 lambs, at 6 shillings a
head ?
3. What will 9 pounds of sugar cost, at 9
cents a pound ]
4. If Maria write 4 lines a day, how
many lines will she write in 9 days I
5. There are 10 dollars in one eagle; how
many dollars in 4 eagles 1
6. At 3 cents a skein, what will be the
cost of 9 skeins of silk I
7. If a man consume 8 pounds of meat in
a week, how much will he consume in 9
weeks ?
8. If it take 7 yards of calico to make one
dress, how many yards will it take to make
9 dresses I
9. What cost 9 hats at 3 dollars apiece ?
10. What cost 9 pounds of nails, at 6
cents a pound I
46 MULTIPLICATION.
LE SSON XI.
10 times 1 are 10
10 times 2 are 20
10 times 3 are 30
10 times 4 are 40
10 times 5 are 50
10 times 6 are 60
10 times 7 are 70
10 times 8 are 80
10 times 9 are 90
10 times 10 are 100
1. If a barrel of apples is worth 9 shil-
lings, what are 10 barrels worth ?
2. At 5 dollars a yard, what are 10 yards
of broadcloth worth ?
3. What will be the cost of 10 cords of
wood, at 3 dollars a cord ?
4. What will be the cost of 10 yards of
calico, at 10 cents a yard?
5. If a man earn 8 shillings a day, how
much will he earn in 10 days?
6.* If Margaret earn 7 shillings a week,
how much will she earn in 10 weeks ?
7. In an orchard are 10 rows of trees,
and 6 trees in each row; how many trees
in the orchard ?
8. Ellen paid 4 shillings a yard for 10
yards of delaine ; what did the whole cost?
9. What cost 10 bushels of potatoes, at 2
shillings a bushel ?
10. What cost 10 pounds of sugar at 10
cents a pound ?
_ J
MULTIPLICATION. 47
LE SSC
PROMISCUO
2 times 8 are how many?
3 times 9 are how many ?
4 times 8 are how many?
7 times 5 are how many ?
9 times 4 are how many ?
6 times 3 are how many?
4 times 9 are how many?
3 times 4 are how many?
5 times 9 are how many ?
7 times 6 are how many?
>N XII.
US REVIEW.
2 times 9 are how many?
8 times 2 are how 'many ?
6 times 5 are how many?
4 times 7 are how many ?
9 times 3 are how many?
5 times 7 are how many?
5 times 8 are how many?
9 times 5 are how many?
6 times 4 are how many ?
8 times 3 are how many?
3 times 7 are how many?
8 times 9 are how many ?
6 times 8 are how many?
5 times 6 are how many ?
7 times 3 are how many ?
6 times 6 are how many ?
9 times 7 are how many ?
3 times 8 are how many ?
4 times 6 are how many?
7 times 4 are how many?
5 times 2 are how many?
7 times 7 are how many ? (
4 times 2 are how many ?
9 times 9 are how many ?
4 times 3 are* how many?
6 times 9 are how many ?
2 times 6 are how many?
8 times 5 are how many ?
4 times 4 are how many ?
9 times 8 are now many?
8 times 7 are how many?
5 times 4 are how many?
3 times 5 are how many?
3 times 4 are how many?
2 times 5 are how many ?
8 times 6 are how many ?
7 times 8 are how many?
5 times 3 are how many?
3 times 6 are how many?
8 times 8 are how many ?
7 times 0 are how many?
2 times 4 are how many ?
5 times 9 are how many ?
9 times 8 are how many?
3 times 3 are how many ?
2 times 3 are how many ?
7 times 4 are how many ?
0 times 8 are how many ?
3 times 6 are how many ?
6 times 10 are how many?
48 MULTIPLICATION.
LESSON XIII.
PROMISCUOUS EXAMPLES.
1. If one ream of paper cost 5 dollars,
what* will 9 reams cost]
ANALYSIS. — If 1 ream of paper cost 5 dollars, 9
reams, which are 9 times 1 ream, will cost 9 times 5 dol-
lars, which are 45 dollars. Therefore, fyc.
2. At 4 dollars apiece, what is the value
of 3 satin vests 1 of 6 I of 8 ? of 7 ?
3. A man bought 5 brooms, at 2 shillings
apiece, and 2 gallons of molasses at 4 shil-
lings a gallon; what was the cost of the
whole I
4. At 9 dollars a month, how much will a
man earn in 4 months I in 6 months ? in 7
months'? in 9 months'?
5. Bought 5 cords of wood at 3 dollars a
cord, and 2 tons of hay at 7 dollars a ton;
which cost the most, and how much]
6. How much is 6 times 9 less 4 ? 8 times
7 less 6 ? 4 times 7 less 8 ? 7 times 7 less 9 I
7. Which is less, 6 times 8, or 5 times
9 ? 4 times 10, or 5 times 8 ? 3 times 9, or
5 times 6 ?
8. Peter sold his knife for 30 cents, and
received in payment 3 quarts of chestnuts at
8 cents a quart, and the remainder in money ;
how much money did he receive?
DIVISION.
49
LESSON I.
DIVISION is finding how many times one number or
quantity is contained in another : thus,
1. How many churches will three bells supply, if each
church has one bell ?
One is contained in three how many times?
2. If one man can make 2 axes in one day, how many
days will it take him to make 4 axes ?
Two is contained in four how many times ?
3. A lady gave 6 dolls to some children, giving them
2 apiece ; to how many children did she give the dolls ?
Two is contained in six how many times ?
4. If a chair-maker can make 3 chairs in a day, how
many days will it take him to make 9 chairs ?
Three is contained in nine how many times ?
5. James gave 8 bunches of grapes to his sisters, giv-
ing them 4 bunches each ; how many sisters had he ?
Four is contained in eight how many times ?
50
DIVISION.
1
LESSON I
I.
1
in
1, 1
time
1
in
6,
6
times
1
in
2, 2
times
1
in
7,
7
times
1
in
3, 3
times
1
in
8,
8
times
1
in
4, 4
times
1
in
9,
9
times
1
in
5, 5
times
1
in
10,
10
times
2
in
2,
1 time
2
in
12,
6
times
2
in
4,
2 times
2
in
14,
7
times
2
in
6,
3 times
2
in
16,
8
times
2
in
8,
4 times
2
in
18,
9
times
2
in
10,
5 times
2
in
20,
10
times
1. At 2 cents apiece, how many peaches
can be bought for 6 cents ?
ANALYSIS. — Since 2 cents will buy 1 peach, 6 cents
will buy as many peaches as 2 cents, the price of 1 peach,
is contained times in 6 cents, which are 3 times. There-
fore, at 2 cents apiece, 3 peaches can be bought for 6 cents.
2. At 2 cents apiece, how many oranges
can you buy for 8 cents ? for 16 cents ?
3. If a man walk 2 miles an hour, how
long will it take him to walk 14 miles?
4. At 2 shillings a bushel, how many
bushels of apples can be bought for 18 shil-
lings 1
5. At 1 dollar a yard, how many yards of
cloth can be bought for 9 dollars ]
DIVISION.
51
LESSON III.
3 in
3 in
3 in
3, 1 time
6, 2 times
9, 3 times
3 in 12, 4 times
3 in 15, 5 times
3 in 18, 6 times
3 in 21, 7 times
3 in 24, 8 times
3 in 27, 9 times
3 in 30, 10 times
1. At 3 dollars a cord, how many cords
of wood can be bought for 12 dollars ?
ANALYSIS. — Since 3 dollars will buy 1 cord, 12 dol-
lars will buy as many cords as 3 dollars, the price of
1 cord, is contained times in 12 dollars, which are 4
times. Therefore, at 3 dollars a cord, 4 cords of wood
can be bought for 12 dollars.
2. For 21 cents, how many yards of rib-
bon can you buy, at 3 cents a yard ?
3. If the cars run a mile in 3 minutes,
how many miles will they run in 30 min-
utes I
4. A father divided 24 marbles among his
3 boys ; how many did he give to each ?
5. How many lemons, at 3 cents apiece,
can be bought for 18 cents ]
6. At 3 cents a quart, how many quarts
of milk can be bought for 27 cents I
7. Harriet paid 3 cents a spool for some
thread ; how many spools could she buy for
15 cents ?
52
DIVISION.
IV,
4 in 4, 1 time
4 in 8, 2 times
4 in 12, 3 times
4 in 16, 4 times
4 in 20, 5 times
LESSON
4 in 24,
4 in 28,
4 in 32,
4 in 36,
6 times
7 times
8 times
9 times
4 in 40, 10 times
1. If 4 boys can sit on one seat, how many
seats will accommodate 20 boys 1
2. If a class of 4 boys answer 28 ques-
tions, how many will each answer ]
3. Clinton earned 40 cents in 4 days ; how
many cents did he earn in one day?
4. If bonnets are 4 dollars apiece, how
many can be bought for 20 dollars'?
5. Mary gave 36 cents for 4 yards of rib-
bon ; how much was it a yard 1
6. If 4 benches will accommodate 24
pupils, how many must sit on each bench ?
7. If you put 32 sheep into 4 pens, how
many must you put into each pen ?
8. Helen paid 4 shillings a yard for lace ;
how many yards could she buy for 16 shil-
lings ?
9. At 4 dimes apiece, how many books
can be bought for 24 d.mes \
10. Carrie gave 12 cents for 4 skeins of
silk ; how much was it a skein ?
DIVISION.
53
LESSON V.
5 in 5, 1 time
5 in 10, 2 times
5 in 15, 3 times
5 in 20, 4 times
5 in 25, 5 times
5 in 30, 6 times
5 in 35, 7 times
5 in 40, 8 times
5 in 45, 9 times
5 in 50, 10 times
1. A man has 30 dollars, which he wishes
to lay out in flour at 5 dollars a barrel ; how
many barrels can he buy 1
2. If I pay 10 cents for riding 5 miles in
the cars, how much is that a mile ]
3. George wishes to divide 15 apples
among 5 boys ; how many must he give to
each ?
4. In a school of 35 pupils, there were 5
classes ; how many pupils in a class ?
5. How many tons of coal, at 5 dollars a
ton, can a blacksmith purchase for 40 dol-
lars ?
6. How long will it take a man to drive
50 miles, with a horse and carriage, if he
drive 5 miles an hour ?
7. How many pounds of tea, at 5 shillings
a pound, can be bought fot 20 shillings \
8. Henry gave 45 cents to 5 poor chil-
dren ; how many cents did he give to each
child ]
54
DIVISION.
LESSON VI.
6 in 6, 1 time
6 in 12, 2 times
6 in 18, 3 times
6 in 24, 4 times
6 in 30, 5 times
6 in 36, 6 times
6 in 42, 7 times
6 in 48, 8 times
6 in 54, 9 times
6 in 60, 10 times
1. If a man can dig 48 rods of ditch in
6 days, how many rods can he dig in one
day?
2. In New England, 6 shillings make one
dollar; how many dollars in 30 shillings'?
3. At 6 cents a pound, how many pounds
of lard can be bought for 54 cents 1
4. Burton sold 6 quarts of cherries for 36
cents ; how much did he get a quart ?
5. If a man build 42 rods of fence in 6
days, how many rods can he build in one
day ?
6. How long will it take you to read 60
pages, if you read 6 pages a day ?
7. If 6 bushels of rye cost 6 dollars, how
much is that a bushel I
8. If a steamboat run 6 miles an hour,
how long will it take her to run 24 miles ?
9. When crackers are 6 cents a pound,
how many pounds can be bought for 18
cents ?
DIVISION. 55
LESSON VII.
7 in 7, 1 time
7 in 14, 2 times
7 in 21, 3 times
7 in 28, 4 times
7 in 35, 5 times
7 in 42, 6 times
7 in 49, 7 times
7 in 56, 8 times
7 in 63, 9 times
7 in 70, 10 times
1. How many yards of cloth, at 7 shillings
a yard, can be bought for 42 shillings 1
2. A farmer sold 7 sheep for 14 dollars ;
how much* did he receive apiece?
3. Seth sold his sled for 35 cents; how
many slates, at 7 cents apiece, can he buy
for the money ?
4. If 7 yards of calico will make a dress,
how many dresses can be made from a piece
containing 28 yards?
5. In one week there are 7 days ; how
many weeks in 21 days? in 28 days? in
56 days ? in 70 days ?
6. Levi paid 7 cents for 7 slate pencils ;
how much did he pay apiece ?
7. If a man can build 49 rods of stone
wall in 7 days, how much can he build in
1 day?
8. When hops are 7 cents a pound, how
many pounds can be bought for 70 cents?
9. How many times 7 in 63 ?
56
DIVISION.
LESSON VIII.
8 in 8, 1 time
8 in 16, 2 times
8 in 24, 3 times
8 in 32, 4 times
8 in 80, 10 times
8 in 48, 6 times
8 in 56, 7 times
8 in 64, 8 times
8 in 72, 9 times
8 in 40, 5 times
1. Giles can buy a hoop for 8 cents; how
many hoops" can he buy for 40 cents ?
2. A man paid 72 cents for 8 pounds of
sugar; what was the price of one pound?
3. How many bins will be required to
hold 56 bushels of oats, if each bin hold 8
bushels ?
4. At 8 dollars a ton, how many tons of
hay can be bought for 64 dollars ]
5. A farmer sold 8 barrels of apples for
24 dollars ; how much did he receive for one
barrel ?
6. If there are 8 trees in each row, how
many rows are there in an orchard contain-
ing 80 trees ?
7. How many spelling books, at 8 cents
apiece, can you buy for 48 cents'? •
8. A laborer received 16 dollars for 8
days' work ; how much was that a day ?
9. James bought 8 lemons for 32 cents ;
what was the cost of one lemon ?
DIVISION.
57
9 in 9, 1 time
9 in 18, 2 times
9 in 27, 3 times
9 in 36, 4 times
9 in 45, 5 times
LESSON IX
9 in 54,
9 in 63,
9 in 72,
9 in 81,
6 times
7 times
8 times
9 times
9 in 90, 10 times
1. How many classes, of 9 pupils each,
can be formed of 45 pupils ?
2. When eggs are 9 cents a dozen, how
many dozen can be bought for 63 cents ?
3. A class of 9 'pupils present their teacher
with a book which cost 90 cents ; how
many cents must each pay towards the
book]
4. If you travel 9 miles an hour, how long
will it take you to travel 81 miles 1
5. A farmer distributed 9 bushels of pota-
toes equally among 9 poor families; how
many did he give to each I
6. If a man spend 9 cents a day for cigars,
how long will 54 cents last him ?
7. For 72 shillings, how many yards of
silk can a lad 7 buy at 9 shillings a yard ?
8. William sold 9 quarts of cherries for
36 cents ; how much did he receive a quart?
9. How many tons of hay, at 9 dollars a
ton, can be bought for 18 dollars ?
58
DIVISION.
10
10
10
10
10
in
in
in
in
in
10,
20,
30,
40,
50,
LESS
1 time
2 times
3 times
4 times
5 times
ON
10
10
10
10
10
X.
in 60,
in 70,
in 80,
in 90,
in 100,
6
7
8
9
10
times
times
times
times
times
1. When butter is 10 cents a pound, how
many pounds can I buy for 80 cents ?
2. At 10 dollars an acre, how many acres
of land can be bought for 100 dollars ?
3. How long will it take a boy to earn 90
cents, if he earn 10 cents a day ?
4. In one dime are 10 cents; how many
dimes in 30 cents I
5. At 10 shillings apiece, how many glass
lamps can be bought for 50 shillings ?
6. How long will it take you to read 70
pages, if you read 10 pages a day ?
7. When shawls are 10 dollars apiece, how
many can be bought for 60 dollars I
8. How long will it take you to earn 40
dollars, if you earn 10 dollars a month?
9. If one man can build 10 rods of fence
in one day, how many men will it take to
build 20 rods in the same time 1
10. At 10 cents apiece, how many melons
can be bought for 40 cents ?
DIVISION. 59
LESS<
PROMISCUO
6 in 36, how many times ?
7 in 42, how many times ?
j 6 in 18, how many times?
9 in 81, how many times?
5 in 35, how many times ?
8 in 72, how many times?
9 in 27, how many times ?
4 in 20, how many times ?
3 in 18, how many times?
6 in 54, how many times ?
3N XI.
[JS REVIEW.
3 in 15, how many times?
5 in 25, how many times?
9 in 63, how many times ?
6 in 12, how many times?
7 in 28, how many times?
4 in 16, how many times?
7 in 49, how many times ?
4 in ? 6, how many times ?
8 in 64, how many times?
8 in 40, how many times ?
8 in 24, how many times?
5 in 45, how many times?
6 in 42, how many times ?
8 in 56, how many times?
9 in 18, how many times?
5 in 40, how many times?
7 in 63, how many times?
3 in 27, how many times?
7 in 21, how many times?
1 8 in 16, how many times?
3 in 12, how many times?
4 in 28, how many times ?
8 in 32, how many times ?
6 in 48, how many times ?
2 in 14, how many times?
9 in 45, how many times ?
8 in 48, how many times?
7 in 56, how many times ?
3 in 21, how many times ?
6 in 54, how many times ?
8 in 8, how many times?
4 in 12, how many times?
7 in 35, how many times?
5 in 10, how many times?
7 in 14, how many times?
2 in 6, how many times ?
4 in 24, how many times?
5 in 30, how many times?
9 in 36, how many times?
6 in 30, how many times?
3 in 24, how many times ?
2 in 16, how many times ?
4 in 32, how many times ?
6 in 24, how many times ?
9 in 72, how many times?
5 in 10, how many times?
4 in 8, how many times ?
5 in 20, how many times?
2 in 10, how many times?
7 in 7, how many times?
60 DIVISION.
LESSON XII.
PROMISCUOUS EXAMPLES.
1. When flour is 7 dollars a barrel, how
many barrels can be bought for 63 dollars ]
ANALYSIS. — Since 7 dollars will buy I barrel, 63
dollars will buy as many barrels as 7 dollars, the price
of 1 barrel, is contained times in 63 dollars, which are
9 times. Therefore, fyc.
2. If it take Cl bushels of apples to make
9 barrels of cider, how many bushels will
make one barrel I
3. How long will it take 5 men to do a
job of work that one man can do in 30 days I
4. How long will 12 dollars pay for my
board, at the rate of 6 dollars a week I
5. If 54 pounds of provision last one man
9 days, how many pounds would last him
one day I
6. Marcus read 100 pages in 10 days;
how many pages did he read each day ]
7. A cabinet maker received 45 dollars for
some chairs at 5 dollars apiece ; how many
chairs did he sell I
8. If one man can mow a field of grass in
18 days, in what time would 6 men mow the
same ]
9. A farmer sold some hay for 30 dollars,
and took 10 sheep for payment; what was
the cost of each sheep ?
PROMISCUOUS REVIEW. 61
LESSON XIII.
1. How many tons of hay, at 6 dollars a
ton, will pay for 8 yards of broadcloth, at 3
dollars a yard ?
ANALYSTS. — As many tons of hay at 6 dollars a ton,
as 6 dollars, the price of a ton, is contained times in
8 times 3 dollars, or 24 dollars, the cost of the broad-
cloth, which are 4 times. TJterefore 4 tons of hay, at
6 dollars a ton, will pay for 8 yards of broadcloth, at 3
dollars a yard.
2. How many dozen of eggs, at 9 cents a
dozen, will pay for 6 yards of calico, at 6
cents a yard ?
3. Charles sold 6 quarts of beech nuts, at
4 cents a quart, and took his pay in oranges,
at 3 cents apiece ; how many oranges did he
receive ?
4. At 6 dollars a barrel, how many bar-
rels of flour will pay for 3 barrels of pork,
at 10 dollars a barrel I
5. If 5 men can hoe a field of corn in 6
days, how long will it take one man ?
6. If 8 men can build a shed in 10 days,
how many men must be employed to build it
in one day]
7. If 4 men can do a piece of work in 7
days, how long will it take one man to do it?
8. How many days' labor, at 8 shillings
a day, will pay for 10 bushels of potatoes at
4 shillings a bushel ?
62 PROMISCUOUS REVIEW.
LESSON XIV.
1. If 7 oranges cost 28 cents, what will 3
oranges cost I
ANALYSIS. — If 7 oranges cost 28 cents, I orange
will cost as mang cents as 7 is contained times in 28,
which is 4 times ; 3 oranges, which are 3 times 1 orange,
will cost 3 times 4 cents, or 12 cents. Therefore^ if 7
oranges cost 28 cents, 3 oranges will cost 12 cents.
2. If 6 pounds of sugar cost 60 cents,
what will 9 pounds cost?
3. A farmer sells 8 sheep for 24 dollars ;
how much does he receive for 5 sheep ?
4. If a man can earn 72 dollars in 8
weeks, how much can he earn in 10 weeks ?
5. Jane bought 5 steel pens for 15 cents;
what would be the cost of 10 pens at the
same rate ?
6. A grocer sold 10 pounds of tea for 40
shillings ; what would be the cost of 8
pounds at the same rate ?
7. If a man can chop 16 cords of wood in
8 days, how much can he chop in 3 days 1
in 5 days'? in 7 days? in 10 days'? in 12
days ?
8. If 7 yards of calico cost 63 cents, what
will 3 yards cost? 5 yards? 6 yards? 9
yards? 10 yards ?
9. When 4 cords of wood are worth 20
dollars, what will 9 cords be worth ?
PROMISCUOUS REVIEW. 63
LESSON XV.
1. Isabel had 15 pinks, and gave 6 to
Clara, and 4 to Herbert ; how many did she
keep for herself?
ANALYSIS. — She kept as many pinks as the difference
between 15 pinks and the sum of 6 pinks and 4 pinks ;
6 and 4 are 10, and 10 from 15 leaves 5. Therefore,
if Isabel had 15 pinks, and gave away 10, she had 5 left.
2. Lucian, having 20 marbles, gave 9 to
Henry, and 6 to John ; how many had he
left!
3. From a piece of cloth containing 12
yards, 5 yards were cut for a coat, 3 yards
for a pair of pantaloons, and 1 yard for a
vest ; how many yards were left?
4. If 2 men start from the same place and
travel in opposite directions, one at the rate of
4 miles an hour, and the other at the rate of
5 miles an hour, how far apart will they be
at the end of 1 hour ? At the end of 2 hours ?
5 hours'? 6 hours? 8 hours? 10 hours?
5. A grocer sold 2 pounds of rice at 6
cents a pound, a pound of soda for 8 cents,
and a bar of soap for 7 cents, and was
paid in eggs at 9 cents a dozen; how many
dozen of eggs did he receive ?
6. If a man travel 36 miles in 9 hours,
how far will he travel in 5 hours? in 6
hours ? in 7 hours ?
64
FRACTIONS.
LESSON I.
When a unit or whole thing is divided into two or
more equal parts, those parts are called FRACTIONS.
1. If a yard measure be divided into two equal parts,
one of the parts is called one half.
How many halves make a whole thing? Am. Two.
2. If a yard measure be divided into three equal
parts, one of the parts is called one third.
How many thirds make a whole thing ? Ans. Three.
3. If a yard measure be divided into^bwr equal parts,
one of the parts is called one fourth, two of the parts
two fourths, three of the parts three fourths.
.-ONEFXHI.RTH.
DUE FOU:R±H
Ans.
How many fourths make a whole thing?
Four.
4. If a yard measure be divided into five equal parts,
one of the parts is called one fifth, two of the parts
two fifths, three of the parts three fifths, four of the parts
four fifths.
-'ONE FI*TH JONCJrJ
How many fifths make a whole thing? Ans. Five.
5. If a yard measure be divided into six equal parts,
one of the parts is called one sixth, two of the parts two
sixths, and so on.
^ggPFCH:- :ijHEL&LXTM QKLESLXTH ON f- SIXTH , ONES IXT-H ONE-SIXTH
How many sixths make a whole thing ? Ans. Six.
FRACTIONS. 65
LESSON II.
1. If any number or whole thing be divided
into seven equal parts, one of the parts is
called one seventh, two of the parts two
sevenths, and so on.
* How many sevenths make a whole thing I
Ans. Seven sevenths.
2. If any number or thing be divided into
eight equal parts, one of the parts is called
one eighth, five of the parts five eighths, and
so on.
How many eighths make a whole thing ]
Ans. Eight eighths.
3. If any number or thing be divided into
nine equal parts, one of the parts is called
one ninth, seven of the parts seven ninths,
and so on.
How many ninths make a whole thing?
How many tenths make a whole thing]
The following is the method of expressing
fractions by figures : —
i, one half.
i, one third.
i, one fourth.
i, one fifth.
I, one sixth.
I, one seventh.
, one eighth.
, one ninth.
, one tenth.
NOTE. — In any fraction, as f, (two thirds,) the num-
ber below the line is called the Denominator, and it
shows into how many equal parts the whole number or
thing is divided. The number above the line is called
the Numerator, and it shows the number of parts that
are used, or that are expressed by the fraction.
66 FRACTIONS.
LESSON III.
1. What do you understand by i of any
number or thing ?
Ans. One of the two equal parts into which
the number or thing is divided.
2. What do you understand by i of any
number or thing!
Ans. One of the three equal parts into
which the number or thing is divided.
3. What do you understand by § of any
number or thing!
Ans. Two of the three equal parts into
which the number or thing is divided.
4. How do you find $ of any number?
Ans. Divide the given number by 2.
5. How do you find i of any number?
Ans. Divide the given number by 3.
6. How, then, will you find i of any num-
ber ? how i ? how i ? how I ? how i ? how
i? howA?
7. AVhat do you understand by i of any
number or thing ? by 1 1 by f ? by 1 1 by i ?
byH by*? by H by f] by I? by H byi?
byH
9. What is i of 4? of 6? of 8? of 10?
of 1G? of 20?
10. What is i of 8? of 12? of 16? of 20?
of 28?
11. What is i of 12? of24? of36?
FRACTIONS. 67
LESSON IV.
1. In 1 orange, how many halves?
2. In 3 oranges, how many halves ]
ANALYSIS. — Since in 1 orange there are 2 halves, in
3 oranges there are 3 times 2 halves, which are 6 halves.
Therefore, in 3 oranges there are 6 halves.
3. How do you find how many halves
there are in any number or thing I
Ans. Multiply the whole number by 2.
4. How do you find how many thirds
there are in any number or thing]
Ans. Multiply the whole number by 3.
5. How many halves are there in 4 pears ]
in 4 pears and 1 half ] in 5 pears ]
6. In 6 bushels and 1 half, how many
halves ]
7. In 3 apples, how many thirds ]
8. In 4 apples and 1 third, how many
thirds are there I in 4 and 2 thirds I in 5 ]
in 5 and 1 third ]
9. How many halves in 7 ] in 7 and 1
half] in 8? in 9 and 1 half] in 101
10. How many thirds in 5 1 in 5 and 1
third 1 in 5 and 2 thirds ] in 6 1 in 7 and
1 third! in 7 and 2 thirds'?
11. In 8 dollars, how many halves ] how
many thirds ]
1 2. How many half miles, in 7 miles and
1 half]
68 FRACTIONS.
LESSON V.
1. In 5 bushels, how many fourths ]
ANALYSIS. — Since in 1 bushel there are 4 fourths,
in 5 bushels there are 5 times 4 fourths, which are 20
fourths. Therefore, in 5 bushels there are 20 fourths.
2. How many fourths in 6? in 6 and 1
fourth^ in 6 and 3 fourths? in 7 and 1
fourth ] in 8 and 3 fourths I in 9 I
3. How many fifths in 2 ] in 3 ] in 4 arid
1 fifth ] in 5 and 2 fifths] in 7 and 3 fifths]
4. How many sixths in 1 ] in 2] in 4]
in 4 and 1 sixth] in 7 and 2 sixths] in 7
and 5 sixths ]
5. In 3, how many sevenths ] in 3 and 5
sevenths] in 4 and 1 seventh] in 4 and 4
sevenths ]
6. In 7, how many sevenths ] in 7 and 6
sevenths ]
7. How many eighths in 2] in 3] in 5
and 1 eighth ] in 5 and 7 eighths ]
8. In 1, how many ninths] in 2] in 5 ]
in 6 ] in 4 and 3 ninths ] in 7 and 5 ninths ]
in 8]
9. How many tenths in 1 ] in 2 ] in 3 ]
in 4 and 5 tenths ] in 6 and 3 tenths ] in 9
and 9 tenths ]
10. In 6, how many fifths] how many
sixths] how many sevenths] how many
eighths] how many ninths]
FRACTIONS. 69
LESSON VI.
1. In 6 halves of a mile, how many miles ?
ANALYSIS. — Since there are 2 halves in 1 mile, in 6
halves of a mile there are as many miles as 2 halves
are contained times in 6 halves, which are 3 times.
Therefore, in 6 halves of a mile are 3 miles.
2. How many bushels in 14 halves of a
bushel ?
3. In 12 halves, how many units or whole
ones?
4. How many units in 15 thirds ? in 18
thirds ? in 21 thirds ?
5. How many units in 16 fourths? in
17 fourths? in 18 fourths? in 20 fourths?
in 23 fourths ?
6. In 7 fifths, how many whole ones ? in
10 fifths? in 25 fifths ? in 26 fifths? in 28
fifths?
7. How many times 1 in 18 sixths? in 19
sixths ? in 24 sixths ? in 30 sixths ? in 32
, sixths ?
8. In f how many times 1 ? in -V1 ? in V-
in-V5? in-27°-? in ¥? in¥? in¥?
9. How many times 1 in I ? in J# ? in
V-? in -¥-? in ¥-? in -¥-? in ¥-?
10. How many units in £? in-V0-? inV?
in-V8-? in-295-? in V?
11. In iJ, how many times 1 ? in ?£? in
infj? inn? in ttJ i
70 FRACTIONS.
LESSON VII.
1. George had f of a dollar, and his father
gave him f of a dollar more ; what part of a
dollar had he then I
ANALYSIS. — He had the sum of f of a dollar and f
of a dollar ; § and f make f of a dollar. Therefore,
since George had f of a dollar, and his father gave him
| of a dollar more, he then had | of a dollar.
2. A lady gave f- of an orange to Mary, f
to Sarah, and f to Julia; how many oranges
did she give away I
3. John bought i of a pound of raisins,
and Joseph f of a pound ; how many pounds
did they both buy I
4. A blacksmith bought at one time f of
a ton of coal, at another time I of a ton, at
another time |,of a ton, and at another time
i of a ton ; how many tons did he buy in all ?
5. Samuel paid & of a dollar for a slate,
A- of a dollar for an arithmetic, T7<j for a
reader, and T9o- for a geography and atlas;,
how many dollars did he pay for all ]
6. A man chopped f of a cord of wood in
the forenoon, and I of a cord in the after-
noon ; how much did he chop in a day ?
7. In the sum of ? and f and f and i , how
many whole ones ?
8. In the sum of F and t and I and tr, how
many whole ones ?
FRACTIONS. 71
LESSON VIII.
1. A gentleman, having I of an acre of
land, sold f of an acre ; what part of an acre
had he left I
ANALYSIS. — He ad left the difference between F of
an acre and § of an acre, which is |- of an acre. There-
fore, since a gentleman had | of an acre of land, and
sold % of an acre, he had f of an acre left.
2. Frank spent f of his money, and lost §
of it ; what part of his money had he left 1
3. Oscar bought a pair of skates for T7a of a
dollar, and sold them for i9<i of a dollar ; how
much did he gain by his bargain ?
4. Eugen'e owns t of a kite, and Herbert
the remainder; what part of the kite does
Herbert own ?
5. Clara, having a quire of paper, gave I
of it to Emeline, and f to Caroline; what
part did she keep for herself?
6. If I divide an orange into 5 equal parts,
and give away 3 pieces, what part of the
orange will be left ?
7. A barrel of flour was distributed among
three poor families ; the first received f of a
barrel, the second f of a barrel, and the
third the remainder ; wiiat part of a barrel
did the third receive ?
8. TV and T3<y and & less T^, are how many
tenths ?
72 FRACTIONS.
LESSON IX.
1. 5 is i of what number?
ANALYSTS. — 5 is 1 half of 2 times 5, which are 10.
T/ierefore, 5 w 1 Aa(/"o/ 10.
2. 3 is -J of what number ?
3. 6 is I of what number ?
4. 7 is 1 of what number ?
5. 5 is i of what number ?
6. 9 is | of what number?
7. 8 is | of what number?
8. 4 is TJ of what number?
9. 2 is £ of what number ?
10. A man bought J of a cord of wood
for 2 dollars ; how much will a cord cost, at
the same rate ?
11. If i of a pound of coffee cost 4 cents,
what will a pound cost ?
12. A lady paid 10 cents for J of a yard
of silk ? how much must she pay for a yard ?
13. Homer gave 6 cents to a beggar,
which was i of all he had ; how many cents
had he at first ?
14. A farmer received 5 dollars towards
the payment for a horse, which was £ of
what he sold him for; what was the price
of the horse ?
15. James sold a kite for 4 cents more
than it cost him, and gained just J of what
he gave for it ; what did it cost ?
FRACTIONS. 73
LESSON X.
1. Lester bought I of a pound of raisins
for 5 cents ; what would f- of a pound cost,
at the same rate ?
ANALYSIS. — Since 1 fourth of a pound of raisins
cost 5 cents, 3 fourths of a pound, which are 3 times 1
fourth, will cost 3 times 5 cents, which are 15 cents.
Therefore, since \ of a pound of raisins cost 5 cents,
% of a pound will cost 15 cents.
2. If i of an acre of land cost 6 dollars,
what will f of an acre cost, at the same rate ?
3. There are 5 yards in i of a piece of
cloth ; how many yards in f of the piece ? in
§ of the piece ? in the whole piece ?
4. If i of a barrel of flour cost 2 dollars,
what will f of a barrel cost? what will f
cost? what will 'the whole barrel cost?
5. If I of a bushel of walnuts cost 3 shil-
lings, what will f of a bushel cost? what
will a bushel cost ?
6. Paid 2 dollars for £ of a ton of hay ;
what would be the cost of a ton, at the same
rate ?
7. A man spent 9 dollars in i of a month ;
how much would he spend in f of a month,
at the same rate? how much in a month ?
8. In iV of a dollar are 10 cents; how
many cents in T4u of a dollar? in -/u? in T9iy?
in a whole dollar ?
74
TABLES.
LESSON XI.
TABLES OF MOXEY, WEIGHTS, MEASURES, ETC.
UNITED STATES MONET.
Tho Denominations are, tho Eagle, Dollar Dime, Cent,
and Mill.
10 mills (m.) make 1 cent, marked ct.
10 cents " 1 dime, " d.
10 dimes, or 100 cts. " 1 dollar, " del. or- 8.
10 dollars " 1 eagle, E.
United States or Federal money is tho legal currency of
tho United States.
NOTE. — The mill is not a coin ; it is used only in computations.
CANADA MONEY.
Tho table end denominations aro tho same as thoso of tho
United States money.
NOTE 1. Tho decimal currency was adopted by tho Canadian Parlia-
ment in 1S5S, and tho Act took effect in 1859.
2. Previous t;> the year 1359, the mon*-y of Canada was reckoned ia
pounds, shilling.*, and pence, the same as in England.
PARTS OF ONE DOLLAH.
5 cents = ^
6} cents = 7'ff
8} cents = -^
10 cents = TJ0
12} cents = ^
16] cents = J
20° cents = i
of a doll,
of a doll.
of a doll,
of a doll,
of a doll
of a doll,
of a doll.
25 cents = \ of a doll.
33| cents = -J of a doll.
37} cents = | of a doll.
50 cents = ± of a doll.
62} cents = g of a doll.
75" cents = | of a doll.
87 A cents = £ of a doll.
TABLES. 75
LESSON XII,
ENGLISH MONEY.
The Denominations are, the Pound, Shilling, Penny,
and Farthing.
4 farthings (qr. or far.) make 1 penny, marked d.
12 pence " 1 shilling, " s.
20 shillings " 1 pound, , " £.
5 shillings make 1 crown, " c.
20 shillings " 1 sovereign," Sov.
21 shillings " 1 guinea, " G.
English or Sterling money is tho currency of Great Britain.
VALUE OF SILVER AND GOLD COINS.
$ cts.
4n English shilling is worth . . . 0 24
" *" crown " . . . 1 20
" " sovereign " . . . 4 84
" " pound " . . . 4 84
" " guinea " . . . 5 00
A franc of France . . .019
A five-franc piece " . . , 0 94
TROY WEIGHT.
The Denominations are, the Pound, Ounce, Penny-
weight, and Grain.
24 grains (gr.) make 1 pennyweight, marked pwt.
20 pennyweights " 1 ounce, oz.
12 ounces " 1 pound, " Ib.
Troy weight is used ia. weighing gold, silver, and jewels.
TABLES.
LESSON XIII.
APOTHECARIES' WEIGHT.
The Denominations are, the Pound, Ounce, Dram,
Scruple, and Grain.
20 grains (gr.) make 1 scruple, marked sc. or 3.
3 scruples " 1 dram, " dr. or 3 .
8 drams " 1 ounce, u oz. or | .
12 ounces " 1 pound, " Ib. or g>.
Apothecaries' weight is used in mixing medicines. But
medicines are always bought and sold by avoirdupois weight.
AVOIRDUPOIS WEIGHT.
The Denominations are, the Ton, Hundred, Quarter,
Pound, Ounce, and Dram.
16 drams (dr.) make 1 ounce, marked oz.
16 ounces " 1 pound, " Ib.
25 pounds " 1 quarter, " qr.
4 quarters " 1 hundred pounds " cwt.
20 cvvt.,or2000lbs.u 1 ton " T.
Avoirdupois weight is used for all the ordinary purposes of
weighing.
NOTK. — The long or grot* ton, in -which the quarter becomes 23
pounds, the hundred icright 112 pounds, and the ton 2240 pounds, is
now seldom used except in estimating English goods, nt the IT. 8.
custom-houses, in freighting nnd wholesaling eoal from the Pennsyl-
vania mines, and in the wholesale iron and plaster trade.
The following denominations aro also in uso :
56 pounds make 1 firkin of butter.
196 " " 1 barrel of Hour.
200 " " 1 " " beef, pork, or fish.
280 " " 1 " " salt at N.Y. salt works.
56 " " 1 bushel of " " "
32 " " 1 " " oats.
48 " " 1 " " barley.
56 " " .1 " " corn or rye.
CO ' ; " 1 " " wheat.
TABLES. 77
LESSON XIV.
LIQUID MEASURE
The Denominations are, tho Hogshead, Barrel, Gallon,
QiifcL-i^ Pint, and GUI.
4 gills (gi.) make 1 pint, marked pt.
2 p:nts " 1 quart, qt.
4 quarts " 1 gallon, " gal.
3U gallons " 1 barrel, " bar.
2 barrels, or G3 gals. " 1 hogshead, " hlid.
Liquid Measure i.i used in measuring liquids; as, liquors,
mola,sSv3s, water, etc.
JS.JTE. — Tho tierce, hogshead, pipe, butt, and tun, arc tho names of
casks, and do nut express any fixed or Uelinito measures.
Ale or Beer Measure, formerly used in measuring beer,
ale, and milk, u not a standard measure, and is almost en-
tirely out of uso.
NOTE. — When this Measure is used,
35 gallons make 1 barrel of beer.
54 " or l\ barrels " 1 hogshead "
DRY "MEASURE.
The Denominations are, tho Chaldron, Bushel, Peck,
Quart, and Pint.
2 pints (pt.) make 1 quart, marked qt.
8 quarts " 1 peck, pk.
4 pecks " 1 bushel, bu.
30 bushels " 1 chaldron of coal, " chal.
Dry Measure is used to measure all kinds of grain, fruits,
roots, coal, salt, seeds, etc.
LONG MEASURE.
The Denominations are the Mile, Furlong, Rod, Yard,
Foot, and Inch.
12 inches (in.) make 1 foot, marked ft.
3 feet " 1 yard, " yd.
51 yards, or 16i ft. " 1 rod or pole, " rd.
40~ rods " 1 furlong, " fur.
8 fur. or 320 rods, u 1 in-le, " in.
Loncj Measure is used in measuring lines or distances.
78 TABLES.
LESSON XV.
NOTE. — Long Measure is used to measure cloth, nrvl other Broods i»oTd
by the yard, tne yar.l being <livi(Je<t into halves, fourths, eighths, uocl
sixteenths. Tue oU table of CLotk Meature \A practically out oi' use.
The following denominations are also in use:
4 inches make 1 hand.
6 feet " 1 fathom.
1.15 statute " 1 geographical mile.
3 geograph. miles," 1 league, marked L.
GO geograph. " " ) d tc ^ 0
69.16 statute " " j l aeoree>
360 degrees make a great circle of the earth.
SQUARE MEASURE.
Tho Denominations arc, tho Square Mile, Acre, Rood,
Square Rod, Sqaaro Foot, and Square Inch.
144 sq. in., (sq. in.) make 1 sq. foot, mkVl sq. ft.
9 squ.ire feet " 1 sq. yard, " sq. yd.
30 1- square yards " -1 sq. rod, " sq. rd.
40 sq. rods or perches " 1 rood, R.
4 roods " 1 acre A.
640 acres " 1 sq. mile, " sq. m.
Square Measure is used in measuring surfaces; as, land,
board.*, plastering, paving, etc.
SURVEYORS' SQUARE MEASURE.
Tho Denominations are, tho Township, Square Mile,
Acre, Square Chain, Square Pole, and Square Link.
G25 square links, (sq.L) make 1 pole, marked P.
16 poles " 1 sq. chain, " sq. ch.
10 square chains " 1 acre, " A.
640 acres " 1 sq. mile, " sq. mi.
33 sq. miles (6 miles sq.) " 1 township," T.
Surveyors' Measure ia used I)/ surveyors, in computing tho
area or contents of lands.
NOTE. — A square mile of land is called a section.
TABLES. 79
LESSON XVI.
CUBIC M E A S U H E .
Tho Denominations are, t'io Cord, Cord Toot, Perch,
Ton, Cu.jic Yard, Cubic Foot, and Cubic Inch.
1728 cubic in. (cu. in.) make 1 cu. foot, mk'd cu. ft.
27 cubic feet " 1 cu. yard, " cu. yd.
40 cu. ft. round timber or ) n , -. ,, ^
50 " "hewn « } 1 ton or load,"
24| cubic feet make 1 perch of stone, Pch.
16 cubic feet " 1 cord foot, mk'd c. ft.
" 1 -d of wood," C.
Cubic Measure is used for measuring solids; as, timber,
wood, stone, etc.
NOTE. — A pile of wood 8 ft. long, 4 ft. wide, and 4 ft. high, contains
1 cord.
MEASURE OF TIME.
The Denominations are, the Century, Tear, Month,
Week, Day, Hour, Minute, and Second.
60 seconds (sec.) make 1 minute, marked m.
60 minutes " 1 hour, ' h.
24 hours " 1 day, ' da.
7 days " 1 week, ' w.
4 weeks " 1 lunar month, ' mo.
52 weeks " 1 year, ' yr.
12 calendar mo. or 365 da. 1 year, l yr.
100 years make 1 century, " C.
Time is the measure of duration, and is used to measure the
exact periods in which events occur.
The following table gives the names of the 12 calendar
months, in their order, and the number of days in each.
1. January has 31 days.
2. February " 28 days.
3. March " 31 days.
4. April " 30 days
5. May " 31 days.
6. June " 30 days.
7. July lias 31 days.
8. August " 31 days.
9. September" 30 days.
10. October " 31 days.
11. November" 30 days.
12. December" 31 days.
80 TABLES.
LESSON XVII.
CIRCULAR MEASURE.
The Denominations are the Circle, Sign, Degree, Minute,
arid Second.
CO seconds (") make 1 minute, marked '•
CO minutes " 1 degree, " , °-
30 degrees " 1 sign, " S-
12 signs,or360deg." the circle of the Zodiac, C.
Circular Measure is applied to the measurement of circles
and angles, and is used by surveyors, navigators, astronomers,
etc., in making their calculations.
MISCELLANEOUS TABLES.
COUNTING.
Tho Denominations are, the Hundred, Score, Great
Gross, Gross, Dozen, and Unit.
12 units or single things make 1 dozen.
12 dozen, or 144 units 1 gross.
12 gros-*, or 144 dozen " 1 great gross.
20 units or single things 1 score.
5 score u 1 hundred.
PAPER.
The Denominations are, the Bale, Bundle, Ream,
Quire, and Sheet.
24 sheets of paper mako 1 quire.
20 quires of paper " 1 ream.
2 reams " 1 bundle.
5 bundles " 1 bale
0 BOOKS.
The Denominations are, Folio, Quarto, Octavo, Duo-
decimo, etc.
A sheet folded in 2 leaves is called a Folio.
A sheet folded in 4 leaves
, r.-,-, -I • an Octavo,
A sheet folded in 8 leaves
()1 o\ O.
« ,-, T . a Duodecimo,
A sheet folded in 12 leaves • Qr ]2mo>
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